Well, at least some of them, others are not so happy about it.
See this interesting New York Times article "Anthropology a Science? Statement Deepens a Rift."
The problem, and I think it is a problem because I believe most fields of study are best when undergirded by the scientific method, is that many cultural/social anthropologists have ideological agendas and see themselves as advocates rather than objective researchers (although, like in many of the social "sciences", there are anthropologists who argue that the whole concept of scientific inquiry is fundamentally flawed since there's no such thing as an objective researcher or absolute truth).
Here's another article Anthropology Without Science at Inside Higher Ed. Check out this quote from the article:
Still, the change seemed to resonate uncomfortably with some more scientifically oriented anthropologists, who perceived a broader shift in the discipline that they say began decades ago. "It’s become so dominated by, not so much humanistic scholars, but by scholars who are actively hostile" to science, said Raymond Hames, chair of anthropology at the University of Nebraska at Lincoln, and a cultural anthropologist who favors a scientific approach.
Here's another quote discussing a sociocultural anthropology PhD student blogger who:
...argued that continuing to use the term "science" in the association's mission statement had become a concern because it maintained "the colonizing, privileging, superior positionality of anthropology that continues to plague the discipline."
In other words, science is a tool of oppression that old white guys use to beat down indiginous cultures.
The article No Science Please, We're Anthropologists in Psychology Today is also interesting and has a number of links to other reactions in the blogosphere.
This controversy caught me eye because, during my first semester at college, I was an anthropology major since I had an interest in archaeology (still do). I remember the professor in my physical anthropology class saying, in a bitter voice, something like "I hope none of you are anthropology majors, there are absolutely no jobs for you when you graduate." Didn't realize it at the time, but it's quite possible he was an adjunct (part-time) instructor - the slave labor of higher education employment.
Anyway, people are complicated, that's why I like studying rocks - doesn't matter if you're Chinese or American, doesn't matter if you're Christian or atheist, doesn't matter if you're male or female, doesn't matter if you're black or white, a granite is a granite. Sure geologists argue over geological interpretations, but the final arbiter is always hard, physical, DATA and not clever ideological arguments.